Mixed-norm Herz-slice Spaces and Their Applications

TL;DR

This paper introduces mixed-norm Herz-slice spaces, unifies existing function spaces, and studies their duals, decompositions, and the boundedness of the Hardy-Littlewood maximal operator within these spaces.

Contribution

It presents the first comprehensive study of mixed-norm Herz-slice spaces, including duality, block decomposition, and operator boundedness results.

Findings

Dual spaces characterized

Block decomposition established

Hardy-Littlewood maximal operator boundedness proved

Abstract

We introduce mixed-norm Herz-slice spaces unifying classical Herz spaces and mixed-norm slice spaces, establish dual spaces and the block decomposition, and prove that the boundedness of Hardy-Littlewood maximal operator on mixed-norm Herz-slice spaces.